1
|
Sowiński T, Ángel García-March M. One-dimensional mixtures of several ultracold atoms: a review. REPORTS ON PROGRESS IN PHYSICS. PHYSICAL SOCIETY (GREAT BRITAIN) 2019; 82:104401. [PMID: 31404916 DOI: 10.1088/1361-6633/ab3a80] [Citation(s) in RCA: 10] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/10/2023]
Abstract
Recent theoretical and experimental progress on studying one-dimensional systems of bosonic, fermionic, and Bose-Fermi mixtures of a few ultracold atoms confined in traps is reviewed in the broad context of mesoscopic quantum physics. We pay special attention to limiting cases of very strong or very weak interactions and transitions between them. For bosonic mixtures, we describe the developments in systems of three and four atoms as well as different extensions to larger numbers of particles. We also briefly review progress in the case of spinor Bose gases of a few atoms. For fermionic mixtures, we discuss a special role of spin and present a detailed discussion of the two- and three-atom cases. We discuss the advantages and disadvantages of different computation methods applied to systems with intermediate interactions. In the case of very strong repulsion, close to the infinite limit, we discuss approaches based on effective spin chain descriptions. We also report on recent studies on higher-spin mixtures and inter-component attractive forces. For both statistics, we pay particular attention to impurity problems and mass imbalance cases. Finally, we describe the recent advances on trapped Bose-Fermi mixtures, which allow for a theoretical combination of previous concepts, well illustrating the importance of quantum statistics and inter-particle interactions. Lastly, we report on fundamental questions related to the subject which we believe will inspire further theoretical developments and experimental verification.
Collapse
Affiliation(s)
- Tomasz Sowiński
- Institute of Physics, Polish Academy of Sciences, Aleja Lotników 32/46, PL-02668 Warsaw, Poland
| | | |
Collapse
|
2
|
Pâţu OI, Klümper A, Foerster A. Universality and Quantum Criticality of the One-Dimensional Spinor Bose Gas. PHYSICAL REVIEW LETTERS 2018; 120:243402. [PMID: 29956958 DOI: 10.1103/physrevlett.120.243402] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/21/2017] [Indexed: 06/08/2023]
Abstract
We investigate the universal thermodynamics of the two-component one-dimensional Bose gas with contact interactions in the vicinity of the quantum critical point separating the vacuum and the ferromagnetic liquid regime. We find that the quantum critical region belongs to the universality class of the spin-degenerate impenetrable particle gas which, surprisingly, is very different from the single-component case and identify its boundaries with the peaks of the specific heat. In addition, we show that the compressibility Wilson ratio, which quantifies the relative strength of thermal and quantum fluctuations, serves as a good discriminator of the quantum regimes near the quantum critical point. Remarkably, in the Tonks-Girardeau regime, the universal contact develops a pronounced minimum, reflected in a counterintuitive narrowing of the momentum distribution as we increase the temperature. This momentum reconstruction, also present at low and intermediate momenta, signals the transition from the ferromagnetic to the spin-incoherent Luttinger liquid phase and can be detected in current experiments with ultracold atomic gases in optical lattices.
Collapse
Affiliation(s)
- Ovidiu I Pâţu
- Institute for Space Sciences, Bucharest-Măgurele, R 077125 Romania
| | - Andreas Klümper
- Fakultät für Mathematik und Naturwissenschaften, Bergische Universität Wuppertal, 42097 Wuppertal, Germany
| | - Angela Foerster
- Instituto de Física da UFRGS, Avenida Bento Gonçalves 9500, Porto Alegre, Rio Grande do Sul, Brazil
| |
Collapse
|
3
|
Petković A, Ristivojevic Z. Spectrum of Elementary Excitations in Galilean-Invariant Integrable Models. PHYSICAL REVIEW LETTERS 2018; 120:165302. [PMID: 29756930 DOI: 10.1103/physrevlett.120.165302] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/18/2017] [Indexed: 06/08/2023]
Abstract
The spectrum of elementary excitations in one-dimensional quantum liquids is generically linear at low momenta. It is characterized by the sound velocity that can be related to the ground-state energy. Here we study the spectrum at higher momenta in Galilean-invariant integrable models. Somewhat surprisingly, we show that the spectrum at arbitrary momentum is fully determined by the properties of the ground state. We find general exact relations for the coefficients of several terms in the expansion of the excitation energy at low momenta and arbitrary interaction and express them in terms of the Luttinger liquid parameter. We apply the obtained formulas to the Lieb-Liniger model and obtain several new results.
Collapse
Affiliation(s)
- Aleksandra Petković
- Laboratoire de Physique Théorique, Université de Toulouse, CNRS, UPS, 31062 Toulouse, France
| | - Zoran Ristivojevic
- Laboratoire de Physique Théorique, Université de Toulouse, CNRS, UPS, 31062 Toulouse, France
| |
Collapse
|
4
|
Petković A, Ristivojevic Z. Dynamics of a Mobile Impurity in a One-Dimensional Bose Liquid. PHYSICAL REVIEW LETTERS 2016; 117:105301. [PMID: 27636481 DOI: 10.1103/physrevlett.117.105301] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/06/2016] [Indexed: 06/06/2023]
Abstract
We develop a microscopic theory of a quantum impurity propagating in a one-dimensional Bose liquid. As a result of scattering off thermally excited quasiparticles, the impurity experiences the friction. We find that, at low temperatures, the resulting force scales either as the fourth or the eighth power of temperature, depending on the system parameters. For temperatures higher than the chemical potential of the Bose liquid, the friction force is a linear function of temperature. Our approach enables us to find the friction force in the crossover region between the two limiting cases. In the integrable case, corresponding to the Yang-Gaudin model, the impurity becomes transparent for quasiparticles and thus the friction force is absent. Our results could be further generalized to study other kinetic phenomena.
Collapse
Affiliation(s)
- Aleksandra Petković
- Laboratoire de Physique Théorique, Université de Toulouse, CNRS, UPS, 31062 Toulouse, France
| | - Zoran Ristivojevic
- Laboratoire de Physique Théorique, Université de Toulouse, CNRS, UPS, 31062 Toulouse, France
| |
Collapse
|
5
|
Massignan P, Levinsen J, Parish MM. Magnetism in Strongly Interacting One-Dimensional Quantum Mixtures. PHYSICAL REVIEW LETTERS 2015; 115:247202. [PMID: 26705652 DOI: 10.1103/physrevlett.115.247202] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/22/2015] [Indexed: 06/05/2023]
Abstract
We consider two species of bosons in one dimension near the Tonks-Girardeau limit of infinite interactions. For the case of equal masses and equal intraspecies interactions, the system can be mapped to a S=1/2 XXZ Heisenberg spin chain, thus allowing one to access different magnetic phases. Using a powerful ansatz developed for the two-component Fermi system, we elucidate the evolution from few to many particles for the experimentally relevant case of an external harmonic confinement. In the few-body limit, we already find clear evidence of both ferromagnetic and antiferromagnetic spin correlations as the ratio of intraspecies and interspecies interactions is varied. Furthermore, we observe the rapid emergence of symmetry-broken magnetic ground states as the particle number is increased. We therefore demonstrate that systems containing only a few bosons are an ideal setting in which to realize the highly sought-after itinerant ferromagnetic phase.
Collapse
Affiliation(s)
- Pietro Massignan
- ICFO-Institut de Ciencies Fotoniques, The Barcelona Institute of Science and Technology, 08860 Castelldefels (Barcelona), Spain
| | - Jesper Levinsen
- School of Physics and Astronomy, Monash University, Victoria 3800, Australia
| | - Meera M Parish
- School of Physics and Astronomy, Monash University, Victoria 3800, Australia
| |
Collapse
|
6
|
Murmann S, Deuretzbacher F, Zürn G, Bjerlin J, Reimann SM, Santos L, Lompe T, Jochim S. Antiferromagnetic Heisenberg Spin Chain of a Few Cold Atoms in a One-Dimensional Trap. PHYSICAL REVIEW LETTERS 2015; 115:215301. [PMID: 26636858 DOI: 10.1103/physrevlett.115.215301] [Citation(s) in RCA: 11] [Impact Index Per Article: 1.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/04/2015] [Indexed: 06/05/2023]
Abstract
We report on the deterministic preparation of antiferromagnetic Heisenberg spin chains consisting of up to four fermionic atoms in a one-dimensional trap. These chains are stabilized by strong repulsive interactions between the two spin components without the need for an external periodic potential. We independently characterize the spin configuration of the chains by measuring the spin orientation of the outermost particle in the trap and by projecting the spatial wave function of one spin component on single-particle trap levels. Our results are in good agreement with a spin-chain model for fermionized particles and with numerically exact diagonalizations of the full few-fermion system.
Collapse
Affiliation(s)
- S Murmann
- Physikalisches Institut der Universität Heidelberg, Im Neuenheimer Feld 226, DE-69120 Heidelberg, Germany
| | - F Deuretzbacher
- Institut für Theoretische Physik, Leibniz Universität Hannover, Appelstraße 2, DE-30167 Hannover, Germany
| | - G Zürn
- Physikalisches Institut der Universität Heidelberg, Im Neuenheimer Feld 226, DE-69120 Heidelberg, Germany
| | - J Bjerlin
- Mathematical Physics and NanoLund, LTH, Lund University, SE-22100 Lund, Sweden
| | - S M Reimann
- Mathematical Physics and NanoLund, LTH, Lund University, SE-22100 Lund, Sweden
| | - L Santos
- Institut für Theoretische Physik, Leibniz Universität Hannover, Appelstraße 2, DE-30167 Hannover, Germany
| | - T Lompe
- Physikalisches Institut der Universität Heidelberg, Im Neuenheimer Feld 226, DE-69120 Heidelberg, Germany
| | - S Jochim
- Physikalisches Institut der Universität Heidelberg, Im Neuenheimer Feld 226, DE-69120 Heidelberg, Germany
| |
Collapse
|
7
|
Levinsen J, Massignan P, Bruun GM, Parish MM. Strong-coupling ansatz for the one-dimensional Fermi gas in a harmonic potential. SCIENCE ADVANCES 2015; 1:e1500197. [PMID: 26601220 PMCID: PMC4646784 DOI: 10.1126/sciadv.1500197] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/12/2015] [Accepted: 05/04/2015] [Indexed: 05/25/2023]
Abstract
A major challenge in modern physics is to accurately describe strongly interacting quantum many-body systems. One-dimensional systems provide fundamental insights because they are often amenable to exact methods. However, no exact solution is known for the experimentally relevant case of external confinement. We propose a powerful ansatz for the one-dimensional Fermi gas in a harmonic potential near the limit of infinite short-range repulsion. For the case of a single impurity in a Fermi sea, we show that our ansatz is indistinguishable from numerically exact results in both the few- and many-body limits. We furthermore derive an effective Heisenberg spin-chain model corresponding to our ansatz, valid for any spin-mixture, within which we obtain the impurity eigenstates analytically. In particular, the classical Pascal's triangle emerges in the expression for the ground-state wave function. As well as providing an important benchmark for strongly correlated physics, our results are relevant for emerging quantum technologies, where a precise knowledge of one-dimensional quantum states is paramount.
Collapse
Affiliation(s)
- Jesper Levinsen
- Aarhus Institute of Advanced Studies, Aarhus University, DK-8000 Aarhus C, Denmark
- School of Physics and Astronomy, Monash University, Clayton, Victoria 3800, Australia
| | - Pietro Massignan
- ICFO—The Institute of Photonic Sciences, 08860 Castelldefels (Barcelona), Spain
| | - Georg M. Bruun
- Department of Physics and Astronomy, Aarhus University, DK-8000 Aarhus C, Denmark
| | - Meera M. Parish
- School of Physics and Astronomy, Monash University, Clayton, Victoria 3800, Australia
- London Centre for Nanotechnology, Gordon Street, London WC1H 0AH, UK
| |
Collapse
|
8
|
Quantum magnetism in strongly interacting one-dimensional spinor Bose systems. Sci Rep 2015; 5:10675. [PMID: 26073680 PMCID: PMC4466587 DOI: 10.1038/srep10675] [Citation(s) in RCA: 38] [Impact Index Per Article: 4.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/30/2014] [Accepted: 04/13/2015] [Indexed: 11/18/2022] Open
Abstract
Strongly interacting one-dimensional quantum systems often behave in a manner that is distinctly different from their higher-dimensional counterparts. When a particle attempts to move in a one-dimensional environment it will unavoidably have to interact and ‘push’ other particles in order to execute a pattern of motion, irrespective of whether the particles are fermions or bosons. A present frontier in both theory and experiment are mixed systems of different species and/or particles with multiple internal degrees of freedom. Here we consider trapped two-component bosons with short-range inter-species interactions much larger than their intra-species interactions and show that they have novel energetic and magnetic properties. In the strongly interacting regime, these systems have energies that are fractions of the basic harmonic oscillator trap quantum and have spatially separated ground states with manifestly ferromagnetic wave functions. Furthermore, we predict excited states that have perfect antiferromagnetic ordering. This holds for both balanced and imbalanced systems, and we show that it is a generic feature as one crosses from few- to many-body systems.
Collapse
|
9
|
Knap M, Mathy CJM, Ganahl M, Zvonarev MB, Demler E. Quantum flutter: signatures and robustness. PHYSICAL REVIEW LETTERS 2014; 112:015302. [PMID: 24483907 DOI: 10.1103/physrevlett.112.015302] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/07/2013] [Indexed: 06/03/2023]
Abstract
We investigate the motion of an impurity particle injected with finite velocity into an interacting one-dimensional quantum gas. Using large-scale numerical simulations based on matrix product states, we observe and quantitatively analyze long-lived oscillations of the impurity momentum around a nonzero saturation value, called quantum flutter. We show that the quantum flutter frequency is equal to the energy difference between two branches of collective excitations of the model. We propose an explanation of the finite saturation momentum of the impurity based on the properties of the edge of the excitation spectrum. Our results indicate that quantum flutter exists away from integrability and provide parameter regions in which it could be observed in experiments with ultracold atoms using currently available technology.
Collapse
Affiliation(s)
- Michael Knap
- Department of Physics, Harvard University, Cambridge, Massachusetts 02138, USA and ITAMP, Harvard-Smithsonian Center for Astrophysics, Cambridge, Massachusetts 02138, USA and Institute of Theoretical and Computational Physics, Graz University of Technology, 8010 Graz, Austria
| | - Charles J M Mathy
- Department of Physics, Harvard University, Cambridge, Massachusetts 02138, USA and ITAMP, Harvard-Smithsonian Center for Astrophysics, Cambridge, Massachusetts 02138, USA
| | - Martin Ganahl
- Institute of Theoretical and Computational Physics, Graz University of Technology, 8010 Graz, Austria
| | - Mikhail B Zvonarev
- Univ Paris-Sud, Laboratoire LPTMS, UMR8626, Orsay, F-91405, France and CNRS, Orsay, F-91405, France
| | - Eugene Demler
- Department of Physics, Harvard University, Cambridge, Massachusetts 02138, USA
| |
Collapse
|
10
|
Zvonarev MB, Cheianov VV, Giamarchi T. Dynamical properties of the one-dimensional spin-1/2 Bose-Hubbard model near a Mott-insulator to ferromagnetic-liquid transition. PHYSICAL REVIEW LETTERS 2009; 103:110401. [PMID: 19792352 DOI: 10.1103/physrevlett.103.110401] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/18/2008] [Revised: 08/10/2009] [Indexed: 05/28/2023]
Abstract
We investigate the dynamics of the one-dimensional strongly repulsive spin-1/2 Bose-Hubbard model for filling nu <or= 1. While at nu=1 the system is a Hubbard-Mott insulator exhibiting dynamical properties of the Heisenberg ferromagnet, at nu<1 it is a ferromagnetic liquid with complex spin dynamics. We find that close to the insulator-liquid transition the system admits for a complete separation of spin and density degrees of freedom valid at all energy and momentum scales within the t-J approximation. This allows us to derive the propagator of transverse spin waves and the shape of the magnon peak in the dynamic spin structure factor.
Collapse
Affiliation(s)
- M B Zvonarev
- DPMC-MaNEP, University of Geneva, 24 quai Ernest-Ansermet, 1211 Geneva 4, Switzerland
| | | | | |
Collapse
|
11
|
Imambekov A, Glazman LI. Phenomenology of one-dimensional quantum liquids beyond the low-energy limit. PHYSICAL REVIEW LETTERS 2009; 102:126405. [PMID: 19392303 DOI: 10.1103/physrevlett.102.126405] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/05/2008] [Indexed: 05/27/2023]
Abstract
We consider the zero temperature behavior of dynamic response functions of 1D systems near edges of support in the momentum-energy plane (k,omega). The description of the singularities of dynamic response functions near an edge epsilon(k) is given by the effective Hamiltonian of a mobile impurity moving in a Luttinger liquid. For Galilean-invariant systems, we relate the parameters of such an effective Hamiltonian to the properties of the function epsilon(k). This allows us to express the exponents which characterize singular response functions of spinless bosonic or fermionic liquids in terms of epsilon(k) and Luttinger liquid parameters for any k. For an antiferromagnetic Heisenberg spin-1/2 chain in a zero magnetic field, SU(2) invariance fixes the exponents from purely phenomenological considerations.
Collapse
Affiliation(s)
- Adilet Imambekov
- Department of Physics, Yale University, New Haven, Connecticut 06520, USA
| | | |
Collapse
|
12
|
Gangardt DM, Kamenev A. Bloch oscillations in a one-dimensional spinor gas. PHYSICAL REVIEW LETTERS 2009; 102:070402. [PMID: 19257649 DOI: 10.1103/physrevlett.102.070402] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/21/2008] [Revised: 01/19/2009] [Indexed: 05/27/2023]
Abstract
A force applied to a spin-flipped particle in a one-dimensional spinor gas may lead to Bloch oscillations of the particle's position and velocity. The existence of Bloch oscillations crucially depends on the viscous friction force exerted by the rest of the gas on the spin excitation. We evaluate the friction in terms of the quantum fluid parameters. In particular, we show that the friction is absent for integrable cases, such as an SU(2) symmetric gas of bosons or fermions. For small deviations from the exact integrability the friction is very weak, opening the possibility to observe Bloch oscillations.
Collapse
Affiliation(s)
- D M Gangardt
- School of Physics and Astronomy, University of Birmingham, Edgbaston, Birmingham, B15 2TT, United Kingdom.
| | | |
Collapse
|